Although we are less interested in counting domino tilings, than we are in generating them. We can of course easily generate domino tilings based on simple repeating patterns, however we are more interested in generating arbitrary domino tilings. If our desire is to uniformly sample from the set of all possible domino tilings, this can be achieved using Markov chains [1]}, [2]}. However as previously stated, we would like to have some influence over the domino tiling we generate.
